connect email server to a web server

Hi all, and sorry if this is the wrong place to ask the following question.

I am building an application where an operator and and a user will be able to communicate to each other with their own control panels (through forms mostly).

A situation has arise where the operator must send an actual real email to the user (meaning that the user will receive it to his inbox raher than to my application inbox). And when the user replies to the operator, comes my problems.

How can i grab the email from the email server (assuming that the user has press " the reply button"),
and store it to my application's database (php, mysql, apache)?

If such a process can be performed, how is it called? How can i search/research/learn more on this?